FFT模板

#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstdio>
#include<queue>
#include<cstring>
#include<ctime>
#include<string>
#include<vector>
#include<map>
#include<list>
#include<set>
#include<stack>
#include<bitset>
#include<unordered_map>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> pii;
typedef pair<ll, ll> pll;
const ll N = 3e6 + 5;
const ll mod = 998244353;
const ll INF = 0x3f3f3f3f;
const ll INF64 = 0x3f3f3f3f3f3f3f3f;
const double gold = (1 + sqrt(5)) / 2.0;
const double PI = acos(-1);
const double eps = 1e-8;
ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a % b); }
ll pow(ll x, ll y, ll mod) { ll ans = 1; while (y) { if (y & 1)ans = (ans * x) % mod; x = (x * x) % mod; y >>= 1; }return ans; }
ll pow(ll x, ll y) { ll ans = 1; while (y) { if (y & 1)ans = (ans * x) % mod; x = (x * x) % mod; y >>= 1; }return ans; }
ll inv(ll x) { return pow(x, mod - 2); }


//使用时记得开大空间2倍以上，开3倍空间
struct complex{
    double x, y;
    complex(double xx = 0, double yy = 0) { x = xx, y = yy; }
};
complex operator + (complex a, complex b) 
{ return complex(a.x + b.x, a.y + b.y); }
complex operator - (complex a, complex b) 
{ return complex(a.x - b.x, a.y - b.y); }
complex operator * (complex a, complex b) 
{ return complex(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x); }


int l, r[N];
int limit = 1;
//type 为1则是DFT，为-1则是IDFT
void FFT(complex *A, int type)
{
    for (int i = 0; i < limit; i++)
        if (i < r[i]) swap(A[i], A[r[i]]); 
    for (int mid = 1; mid < limit; mid <<= 1){
        complex Wn(cos(PI / mid), type*sin(PI / mid));  
        for (int R = mid << 1, j = 0; j < limit; j += R){
            complex w(1, 0);
            for (int k = 0; k < mid; k++, w = w * Wn){
                complex x = A[j + k], y = w * A[j + mid + k];
                A[j + k] = x + y;
                A[j + mid + k] = x - y;
            }
        }
    }
}
complex A[N], B[N];
int CANS[N];
//n和m并不是个数，而是次数，即个数-1
//最后的CANS即为答案
void Convolution(int *a,int n,int *b,int m) {
    //赋值
    for (int i = 0; i <= n; i++)A[i].x = a[i];
    for (int i = 0; i <= m; i++)B[i].x = b[i];
    //补齐为2的k次方
    while (limit <= n + m) limit <<= 1, l++;
    for (int i = 0; i < limit; i++)
        r[i] = (r[i >> 1] >> 1) | ((i & 1) << (l - 1));
    //DFT
    FFT(A, 1);
    FFT(B, 1);
    //计算
    for (int i = 0; i < limit; i++)
        A[i] = A[i] * B[i];
    //IDFT
    FFT(A, -1);
    //按照我们推倒的公式，这里还要除以n
    for (int i = 0; i <= n+m; i++)CANS[i]= (int)(A[i].x / limit + 0.5); 
}
int a[N], b[N];
int main() {
    int n, m,p;
    scanf("%d%d%d", &n, &m,&p);
    for (int i = 0; i <= n; i++)
        scanf("%d", a + i);
    for (int i = 0; i <= m; i++)
        scanf("%d", b + i);
    Convolution(a, n, b, m);
    for (int i = 0; i <= n + m; i++)
        printf("%d ",CANS[i]%p);
    printf("
");


}